data(UCBAdmissions)
Dept=rep(rep(c("A","B","C","D","E","F"),each=2),2)
Gender=rep(rep(c("Male","Female"),6),2)
Count=matrix(UCBAdmissions,ncol=2,byrow=TRUE,dimnames=list(NULL,c("Admit","Reject")))
Admit=rep(c("Yes","No"),each=12)
Frequency=c(Count[,1],Count[,2])
ba=data.frame(Dept,Gender,Admit,Frequency);ba## Dept Gender Admit Frequency
## 1 A Male Yes 512
## 2 A Female Yes 89
## 3 B Male Yes 353
## 4 B Female Yes 17
## 5 C Male Yes 120
## 6 C Female Yes 202
## 7 D Male Yes 138
## 8 D Female Yes 131
## 9 E Male Yes 53
## 10 E Female Yes 94
## 11 F Male Yes 22
## 12 F Female Yes 24
## 13 A Male No 313
## 14 A Female No 19
## 15 B Male No 207
## 16 B Female No 8
## 17 C Male No 205
## 18 C Female No 391
## 19 D Male No 279
## 20 D Female No 244
## 21 E Male No 138
## 22 E Female No 299
## 23 F Male No 351
## 24 F Female No 317UCB.loglin=glm(Frequency~Admit*Gender+Admit*Dept+Gender*Dept,family=poisson,data=ba)
summary(UCB.loglin)##
## Call:
## glm(formula = Frequency ~ Admit * Gender + Admit * Dept + Gender *
## Dept, family = poisson, data = ba)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7
## -0.75481 1.96454 -0.03402 0.15709 1.01273 -0.74367 0.06760
## 8 9 10 11 12 13 14
## -0.06911 1.05578 -0.73617 -0.20117 0.19803 0.99471 -3.15768
## 15 16 17 18 19 20 21
## 0.04449 -0.22034 -0.73839 0.54896 -0.04741 0.05080 -0.61236
## 22 23 24
## 0.42678 0.05113 -0.05370
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.59099 0.11659 30.801 < 2e-16 ***
## AdmitYes 0.68192 0.09911 6.880 5.97e-12 ***
## GenderMale 2.09846 0.11548 18.172 < 2e-16 ***
## DeptB -1.43464 0.23341 -6.146 7.93e-10 ***
## DeptC 2.34983 0.12262 19.163 < 2e-16 ***
## DeptD 1.90293 0.12557 15.154 < 2e-16 ***
## DeptE 2.08467 0.12711 16.400 < 2e-16 ***
## DeptF 2.17093 0.12798 16.963 < 2e-16 ***
## AdmitYes:GenderMale -0.09987 0.08085 -1.235 0.217
## AdmitYes:DeptB -0.04340 0.10984 -0.395 0.693
## AdmitYes:DeptC -1.26260 0.10663 -11.841 < 2e-16 ***
## AdmitYes:DeptD -1.29461 0.10582 -12.234 < 2e-16 ***
## AdmitYes:DeptE -1.73931 0.12611 -13.792 < 2e-16 ***
## AdmitYes:DeptF -3.30648 0.16998 -19.452 < 2e-16 ***
## GenderMale:DeptB 1.07482 0.22861 4.701 2.58e-06 ***
## GenderMale:DeptC -2.66513 0.12609 -21.137 < 2e-16 ***
## GenderMale:DeptD -1.95832 0.12734 -15.379 < 2e-16 ***
## GenderMale:DeptE -2.79519 0.13925 -20.073 < 2e-16 ***
## GenderMale:DeptF -2.00232 0.13571 -14.754 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 2650.095 on 23 degrees of freedom
## Residual deviance: 20.204 on 5 degrees of freedom
## AIC: 217.26
##
## Number of Fisher Scoring iterations: 4Redidual deviance is 20.204 Logit model: exp(??^1 ??? ??^2) = exp(???0.09987) = 0.905 Loglinear model: exp(??^AG11 + ??^AG22 ??? ??^AG12 ??? ??^AG21 ) = exp(???0.09987) = 0.905